This paper considers the argument that if the ban on doping in sports was abolished it would be possible to have doping under medical control, i.e. open doping, prescribed by doctors with collection of reliable information about effects and side-effects. A game-theoretic argument is developed showing that this positive scenario is very unlikely to be instantiated given reasonable assumptions about the motivation of sportspersons and sports doctors. It is furthermore shown that the standard arguments against the current ban on doping also entail that if doping was made legal any requirements that it should be open doping could not be justified